OPENAI MATHEMATICS COLLECTION · FAMILY 240
A CH obstruction to a prescribed categoricity threshold
An AI-generated manuscript. Inclusion does not imply independent verification. View source
Abstract
Assuming the continuum hypothesis, we construct an abstract elementary class with Löwenheim–Skolem number ℵ0 that is categorical in every sufficiently large cardinal but has at least two nonisomorphic models of cardinality \beth_{\omega_2}. Thus categoricity does not transfer down to the proposed bound \beth_{(2^{\aleph_0})^+}, which equals \beth_{\omega_2} under CH. Consequently, if ZFC is consistent, the prescribed-threshold form of Shelah's categoricity conjecture is not provable in ZFC.
Read the source manuscript
The five randomly sampled papers have interactive readers. This catalogue entry links directly to its original PDF.